The converse problem for the multipotentialisation of evolution equations and systems

We propose a method to identify and classify evolution equations and systems that can be multipotentialised in given target equations or target systems. We refer to this as the {\it converse problem}. Although we mainly study a method for $(1+1)$-dimensional equations/system, we do also propose an extension of the methodology to higher-dimensional evolution equations. An important point is that the proposed converse method allows one to identify certain types of auto-B\"acklund transformations for the equations/systems. In this respect we define the {\it triangular-auto-B\"acklund transformation} and derive its connections to the converse problem. Several explicit examples are given. In particular we investigate a class of linearisable third-order evolution equations, a fifth-order symmetry-integrable evolution equation as well as linearisable systems.Comment: 31 Pages, 7 diagrams, submitted for consideratio

Linearisable third order ordinary differential equations and generalised Sundman transformations

We calculate in detail the conditions which allow the most general third order ordinary differential equation to be linearised in X'''(T)=0 under the transformation X(T)=F(x,t), dT=G(x,t)dt. Further generalisations are considered.Comment: 33 page

Anyonic statistics and large horizon diffeomorphisms for Loop Quantum Gravity Black Holes

We investigate the role played by large diffeomorphisms of quantum Isolated Horizons for the statistics of LQG Black Holes by means of their relation to the braid group. To this aim the symmetries of Chern-Simons theory are recapitulated with particular regard to the aforementioned type of diffeomorphisms. For the punctured spherical horizon, these are elements of the mapping class group of $S^2$, which is almost isomorphic to a corresponding braid group on this particular manifold. The mutual exchange of quantum entities in two dimensions is achieved by the braid group, rendering the statistics anyonic. With this we argue that the quantum Isolated Horizon model of LQG based on $SU(2)_k$-Chern-Simons theory explicitly exhibits non-abelian anyonic statistics. In this way a connection to the theory behind the fractional quantum Hall effect and that of topological quantum computation is established, where non-abelian anyons play a significant role.Comment: 20 pages, 8 figures, closest to published versio

A Nonliearly Dispersive Fifth Order Integrable Equation and its Hierarchy

In this paper, we study the properties of a nonlinearly dispersive integrable system of fifth order and its associated hierarchy. We describe a Lax representation for such a system which leads to two infinite series of conserved charges and two hierarchies of equations that share the same conserved charges. We construct two compatible Hamiltonian structures as well as their Casimir functionals. One of the structures has a single Casimir functional while the other has two. This allows us to extend the flows into negative order and clarifies the meaning of two different hierarchies of positive flows. We study the behavior of these systems under a hodograph transformation and show that they are related to the Kaup-Kupershmidt and the Sawada-Kotera equations under appropriate Miura transformations. We also discuss briefly some properties associated with the generalization of second, third and fourth order Lax operators.Comment: 11 pages, LaTex, version to be published in Journal of Nonlinear Mathematical Physics, has expanded discussio

Thermal conductance of thin film YIG determined using Bayesian statistics

Thin film YIG (Y$_3$Fe$_5$O$_{12}$) is a prototypical material for experiments on thermally generated pure spin currents and the spin Seebeck effect. The 3-omega method is an established technique to measure the cross-plane thermal conductance of thin films, but can not be used in YIG/GGG (Ga$_3$Gd$_5$O$_{12}$) systems in its standard form. We use two-dimensional modeling of heat transport and introduce a technique based on Bayesian statistics to evaluate measurement data taken from the 3-omega method. Our analysis method allows us to study materials systems that have not been accessible with the conventionally used 3-omega analysis. Temperature dependent thermal conductance data of thin film YIG are of major importance for experiments in the field of spin-caloritronics. Here we show data between room temperature and 10 K for films covering a wide thickness range as well as the magnetic field effect on the thermal conductance between 10 K and 50 K

The Puzzle of the Flyby Anomaly

Close planetary flybys are frequently employed as a technique to place spacecraft on extreme solar system trajectories that would otherwise require much larger booster vehicles or may not even be feasible when relying solely on chemical propulsion. The theoretical description of the flybys, referred to as gravity assists, is well established. However, there seems to be a lack of understanding of the physical processes occurring during these dynamical events. Radio-metric tracking data received from a number of spacecraft that experienced an Earth gravity assist indicate the presence of an unexpected energy change that happened during the flyby and cannot be explained by the standard methods of modern astrodynamics. This puzzling behavior of several spacecraft has become known as the flyby anomaly. We present the summary of the recent anomalous observations and discuss possible ways to resolve this puzzle.Comment: 6 pages, 1 figure. Accepted for publication by Space Science Review

A nonlocal connection between certain linear and nonlinear ordinary differential equations/oscillators

We explore a nonlocal connection between certain linear and nonlinear ordinary differential equations (ODEs), representing physically important oscillator systems, and identify a class of integrable nonlinear ODEs of any order. We also devise a method to derive explicit general solutions of the nonlinear ODEs. Interestingly, many well known integrable models can be accommodated into our scheme and our procedure thereby provides further understanding of these models.Comment: 12 pages. J. Phys. A: Math. Gen. 39 (2006) in pres

Towards a direct measurement of vacuum magnetic birefringence: PVLAS achievements

Nonlinear effects in vacuum have been predicted but never observed yet directly. The PVLAS collaboration has long been working on an apparatus aimed at detecting such effects by measuring vacuum magnetic birefringence. Unfortunately the sensitivity has been affected by unaccounted noise and systematics since the beginning. A new small prototype ellipsometer has been designed and characterized at the Department of Physics of the University of Ferrara, Italy entirely mounted on a single seismically isolated optical bench. With a finesse F = 414000 and a cavity length L = 0.5 m we have reached the predicted sensitivity of psi = 2x10^-8 1/sqrt(Hz) given the laser power at the output of the ellipsomenter of P = 24 mW. This record result demonstrates the feasibility of reaching such sensitivities and opens the way to designing a dedicated apparatus for a first detection of vacuum magnetic birefringence